Suppose I know that Holly always has a certainty equivalent $\left(x_{C E}\right)$ equal to 0 . Which of the following utility functions describes Holly's preferences? A) $\mathrm{U}(\mathrm{x})=\ln (\mathrm{x})$ B) $\mathrm{U}(\mathrm{x})=\mathrm{x}$ C) $\mathrm{U}(\mathrm{x})=\mathrm{x}$ if $\mathrm{x}0$ and $\mathrm{U}(\mathrm{x})=-2 \mathrm{x}$ if $\mathrm{x}

Question

Suppose I know that Holly always has a certainty equivalent $\left(x_{C E}\right)$ equal to 0 . Which of the following utility functions describes Holly's preferences?
A) $\mathrm{U}(\mathrm{x})=\ln (\mathrm{x})$
B) $\mathrm{U}(\mathrm{x})=\mathrm{x}$
C) $\mathrm{U}(\mathrm{x})=\mathrm{x}$ if $\mathrm{x}>0$ and $\mathrm{U}(\mathrm{x})=-2 \mathrm{x}$ if $\mathrm{x}<=0$
D) $U(x)=\sqrt{x}$

Quizplus · Accepted Answer

The utility function $U(x) = x$ directly translates wealth into utility without any transformation, implying a linear relationship between wealth and utility. This is consistent with a certainty equivalent of 0, as it suggests a risk-neutral behavior where the individual values wealth directly without any adjustment for risk or uncertainty. Other options involve transformations of wealth, implying different attitudes towards risk.

Suppose I Know That Holly Always Has a Certainty Equivalent (xCE)\left(x_{C E}\right)(xCE​)

Suppose I Know That Holly Always Has a Certainty Equivalent $\left(x_{C E}\right)$